Advertisement

Δr in the Two-Higgs-Doublet Model at full one loop level—and beyond

  • David López-ValEmail author
  • Joan Solà
Regular Article - Theoretical Physics

Abstract

After the recent discovery of a Higgs-like boson particle at the CERN LHC-collider, it becomes more necessary than ever to prepare ourselves for identifying its standard or non-standard nature. The fundamental parameter Δr, relating the values of the electroweak gauge boson masses and the Fermi constant, is the traditional observable encoding high precision information of the quantum effects. In this work we present a complete quantitative study of Δr in the framework of the general Two-Higgs-Doublet Model (2HDM). While the one-loop analysis of Δr in this model was carried out long ago, in the first part of our work we consistently incorporate the higher order effects that have been computed since then for the SM part of Δr. Within the on-shell scheme, we find typical corrections leading to shifts of ∼20–40 MeV on the W mass, resulting in a better agreement with its experimentally measured value and in a degree no less significant than in the MSSM case. In the second part of our study we devise a set of effective couplings that capture the dominant higher order genuine 2HDM quantum effects on the δρ part of Δr in the limit of large Higgs boson self-interactions. This limit constitutes a telltale property of the general 2HDM which is unmatched by e.g. the MSSM.

Keywords

Higgs Boson Gauge Boson Minimal Supersymmetric Standard Model Higgs Sector Higgs Boson Masse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The authors are very grateful to Wolfgang Hollik for enlightening conversations on this topic and also for providing useful references. The work of J.S. has been supported in part by the research Grant PA-2010-20807; by the Consolider CPAN project; and also by DIUE/CUR Generalitat de Catalunya under project 2009SGR502.

References

  1. 1.
    J. Incandela, CERN Seminar. Update on the Standard Model Higgs searches in CMS, July 4 2012. CMS-PAS-HIG-12-020 Google Scholar
  2. 2.
    F. Gianotti, CERN Seminar. Update on the Standard Model Higgs searches in ATLAS, July 4 2012. ATLAS-CONF-2012-093 Google Scholar
  3. 3.
    S. Chatrchyan et al. (CMS Collaboration), Phys. Lett. B (2012). arXiv:1207.7235 [hep-ex]
  4. 4.
    G. Aad et al. (ATLAS Collaboration), Phys. Lett. B (2012). arXiv:1207.7214 [hep-ex]
  5. 5.
    P.W. Higgs, Phys. Lett. 12, 132–133 (1964) ADSGoogle Scholar
  6. 6.
    P.W. Higgs, Phys. Rev. Lett. 13, 508–509 (1964) MathSciNetADSGoogle Scholar
  7. 7.
    F. Englert, R. Brout, Phys. Rev. Lett. 13, 321–322 (1964) MathSciNetADSGoogle Scholar
  8. 8.
    G.S. Guralnik, C.R. Hagen, T.W.B. Kibble, Phys. Rev. Lett. 13, 585–587 (1964) ADSGoogle Scholar
  9. 9.
    J.F. Gunion, H.E. Haber, G.L. Kane, S. Dawson, The Higgs Hunter’s Guide (Addison-Wesley, Menlo-Park, 1990) Google Scholar
  10. 10.
    A. Djouadi, Phys. Rep. 457, 1–216 (2008). arXiv:hep-ph/0503172 [hep-ph] ADSGoogle Scholar
  11. 11.
    P.H. Chankowski et al., Nucl. Phys. B, Proc. Suppl. 37, 232–239 (1994) ADSGoogle Scholar
  12. 12.
    R. Barbieri, L. Maiani, Nucl. Phys. B 224, 32 (1983) ADSGoogle Scholar
  13. 13.
    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher, J.P. Silva, Phys. Rep. 516, 1 (2012). arXiv:1106.0034 [hep-ph] ADSGoogle Scholar
  14. 14.
    S. Ferrara (ed.), Supersymmetry, vols. 1–2 (North Holland/World Scientific, Singapore, 1987) Google Scholar
  15. 15.
    D.B. Kaplan, H. Georgi, S. Dimopoulos, Phys. Lett. B 136, 187 (1984) ADSGoogle Scholar
  16. 16.
    K. Agashe, R. Contino, A. Pomarol, Nucl. Phys. B 719, 165–187 (2005). arXiv:hep-ph/0412089 ADSGoogle Scholar
  17. 17.
    J. Mrazek et al., Nucl. Phys. B 853, 1–48 (2011). arXiv:1105.5403 [hep-ph] ADSzbMATHGoogle Scholar
  18. 18.
    G. Burdman, C.E.F. Haluch, J. High Energy Phys. 12, 038 (2011). arXiv:1109.3914 [hep-ph] ADSGoogle Scholar
  19. 19.
    M. Geller, S. Bar-Shalom, A. Soni, arXiv:1302.2915 [hep-ph]
  20. 20.
    M. Schmaltz, D. Tucker-Smith, Annu. Rev. Nucl. Part. Sci. 55, 229–270 (2005). arXiv:hep-ph/0502182 ADSGoogle Scholar
  21. 21.
    M. Perelstein, Prog. Part. Nucl. Phys. 58, 247–291 (2007). arXiv:hep-ph/0512128 ADSGoogle Scholar
  22. 22.
    J.F. Gunion, H.E. Haber, Phys. Rev. D 72, 095002 (2005). arXiv:hep-ph/0506227 ADSGoogle Scholar
  23. 23.
    P.M. Ferreira, H.E. Haber, M. Maniatis, O. Nachtmann, J.P. Silva, Int. J. Mod. Phys. A 26, 769–808 (2011). arXiv:1010.0935 [hep-ph] ADSzbMATHGoogle Scholar
  24. 24.
    E. Ma, Phys. Rev. D 73, 077301 (2006). arXiv:hep-ph/0601225 ADSGoogle Scholar
  25. 25.
    S. Kanemura, Y. Okada, E. Senaha, Phys. Lett. B 606, 361–366 (2005). arXiv:hep-ph/0411354 ADSGoogle Scholar
  26. 26.
    J.M. Cline, K. Kainulainen, M. Trott, J. High Energy Phys. 1111, 089 (2011). arXiv:1107.3559 [hep-ph] ADSGoogle Scholar
  27. 27.
    A. Tranberg, B. Wu, J. High Energy Phys. 1207, 087 (2012). arXiv:1203.5012 [hep-ph] ADSGoogle Scholar
  28. 28.
    B. Stech, Phys. Rev. D 86, 055003 (2012). arXiv:1206.4233 [hep-ph] ADSGoogle Scholar
  29. 29.
    N.G. Deshpande, E. Ma, Phys. Rev. D 18, 2574 (1978) ADSGoogle Scholar
  30. 30.
    R. Barbieri, L.J. Hall, V.S. Rychkov, Phys. Rev. D 74, 015007 (2006). arXiv:hep-ph/0603188 ADSGoogle Scholar
  31. 31.
    E. Lündstrom, M. Gustafsson, J. Edsjö, Phys. Rev. D 79, 035013 (2009). arXiv:0810.3924 [hep-ph] ADSGoogle Scholar
  32. 32.
    A. Arhrib, R. Benbrik, N. Gaur, Phys. Rev. D 85, 095021 (2012). arXiv:1201.2644 [hep-ph] ADSGoogle Scholar
  33. 33.
    L. López-Honorez, E. Nezri, J.F. Oliver, M.H.G. Tytgat, J. Cosmol. Astropart. Phys. 0702, 028 (2007). arXiv:hep-ph/0612275 Google Scholar
  34. 34.
    T. Hambye, M.H.G. Tytgat, Phys. Lett. B 659, 651–655 (2008). arXiv:0707.0633 [hep-ph] ADSGoogle Scholar
  35. 35.
    L. López-Honorez, C.E. Yaguna, J. Cosmol. Astropart. Phys. 1101, 002 (2011). arXiv:1011.1411 [hep-ph] Google Scholar
  36. 36.
    M. Gustafsson, in PoS CHARGED2010 (2010), p. 030 Google Scholar
  37. 37.
    B. Gorczyca, M. Krawczyk, Acta Phys. Pol. B 42, 2229–2236 (2011). arXiv:1112.4356 [hep-ph] Google Scholar
  38. 38.
    M. Krawczyk, D. Sokolowska, Fortschr. Phys. 59, 1098–1102 (2011). arXiv:1105.5529 [hep-ph] zbMATHGoogle Scholar
  39. 39.
    R. Schabinger, J.D. Wells, Phys. Rev. D 72, 093007 (2005). arXiv:hep-ph/0509209 ADSGoogle Scholar
  40. 40.
    B. Patt, F. Wilczek, arXiv:hep-ph/0605188
  41. 41.
    C. Englert, T. Plehn, M. Rauch, D. Zerwas, P.M. Zerwas, Phys. Lett. B 707, 512–516 (2012). arXiv:1112.3007 [hep-ph] ADSGoogle Scholar
  42. 42.
    C. Englert, T. Plehn, D. Zerwas, P.M. Zerwas, Phys. Lett. B 703, 298–305 (2011). arXiv:1106.3097 [hep-ph] ADSGoogle Scholar
  43. 43.
    B. Batell, S. Gori, L.-T. Wang, J. High Energy Phys. 1206, 172 (2012). arXiv:1112.5180 [hep-ph] ADSGoogle Scholar
  44. 44.
    E. Cerveró, J.-M. Gérard, Phys. Lett. B 712, 255–260 (2012). arXiv:1202.1973 [hep-ph] ADSGoogle Scholar
  45. 45.
    J.S. Lee, A. Pilaftsis, Phys. Rev. D 86, 035004 (2012). arXiv:1201.4891 [hep-ph] ADSGoogle Scholar
  46. 46.
    G. Panotopoulos, P. Tuzón, J. High Energy Phys. 07, 039 (2011). arXiv:1102.5726 [hep-ph] ADSGoogle Scholar
  47. 47.
    S. Bar-Shalom, S. Nandi, A. Soni, Phys. Rev. D 84, 053009 (2011). arXiv:1105.6095 [hep-ph] ADSGoogle Scholar
  48. 48.
    A. Arhrib et al., Phys. Rev. D 84, 095005 (2011). arXiv:1105.1925 [hep-ph] ADSGoogle Scholar
  49. 49.
    M. Aoki et al., Phys. Rev. D 84, 055028 (2011). arXiv:1104.3178 [hep-ph] ADSGoogle Scholar
  50. 50.
    S. Chang, J.A. Evans, M.A. Luty, Phys. Rev. D 84, 095030 (2011). arXiv:1107.2398 [hep-ph] ADSGoogle Scholar
  51. 51.
    A. Arhrib, C.-W. Chiang, D.K. Ghosh, R. Santos, arXiv:1112.5527 [hep-ph] (2011)
  52. 52.
    S. Kanemura, K. Tsumura, H. Yokoya, Phys. Rev. D 85, 095001 (2012). arXiv:1111.6089 [hep-ph] ADSGoogle Scholar
  53. 53.
    K. Blum, R.T. D’Agnolo, Phys. Lett. B 714, 66–69 (2012). arXiv:1202.2364 [hep-ph] ADSGoogle Scholar
  54. 54.
    W. Mader, J.-h. Park, G.M. Pruna, D. Stöckinger, A. Straessner, J. High Energy Phys. 1209, 125 (2012). arXiv:1205.2692 [hep-ph] ADSGoogle Scholar
  55. 55.
    N. Craig, J.A. Evans, R. Gray, C. Kilic, M. Park, S. Somalwar, S. Thomas, arXiv:1210.0559 [hep-ph]
  56. 56.
    P.M. Ferreira, R. Santos, M. Sher, J.P. Silva, Phys. Rev. D 85, 077703 (2012). arXiv:1112.3277 [hep-ph] ADSGoogle Scholar
  57. 57.
    P.M. Ferreira, R. Santos, M. Sher, J.P. Silva, Phys. Rev. D 85, 035020 (2012). arXiv:1201.0019 [hep-ph] ADSGoogle Scholar
  58. 58.
    G. Burdman, C.E.F. Haluch, R.D. Matheus, Phys. Rev. D 85, 095016 (2012). arXiv:1112.3961 [hep-ph] ADSGoogle Scholar
  59. 59.
    D. Carmi, A. Falkowski, E. Kuflik, T. Volansky, J. High Energy Phys. 1207, 136 (2012). arXiv:1202.3144 [hep-ph] ADSGoogle Scholar
  60. 60.
    H.S. Cheon, S.K. Kang, arXiv:1207.1083 [hep-ph]
  61. 61.
    N. Craig, S. Thomas, arXiv:1207.4835 [hep-ph]
  62. 62.
    D.S.M. Alves, P.J. Fox, N.J. Weiner, arXiv:1207.5499 [hep-ph]
  63. 63.
    Y. Bai, V. Barger, L.L. Everett, G. Shaughnessy, arXiv:1210.4922 [hep-ph]
  64. 64.
    S. Chang, S.K. Kang, J.-P. Lee, K.Y. Lee, S.C. Park, J. Song, arXiv:1210.3439 [hep-ph]
  65. 65.
    C.-Y. Chen, S. Dawson, arXiv:1301.0309 [hep-ph]
  66. 66.
    W. Altmannshofer, S. Gori, G.D. Kribs, arXiv:1210.2465 [hep-ph]
  67. 67.
    A. Celis, V. Ilisie, A. Pich, arXiv:1302.4022 [hep-ph]
  68. 68.
    W. Hollik, Fortschr. Phys. 38, 165 (1990) Google Scholar
  69. 69.
    W. Hollik, J. Phys. G 29, 131–140 (2003) ADSGoogle Scholar
  70. 70.
    W. Hollik, J. Phys. Conf. Ser. 53, 7–43 (2006) ADSGoogle Scholar
  71. 71.
    W. Hollik, Renormalization of the standard model, in Precision Tests of the Standard Electroweak Model, ed. by P. Langacker. Advanced Series on Directions in High Energy Physics, vol. 14 (World Scientific, Singapore, 1995) Google Scholar
  72. 72.
    J.D. Wells, arXiv:hep-ph/0512342
  73. 73.
    A. Sirlin, A. Ferroglia, arXiv:1210.5296 [hep-ph]
  74. 74.
    The LEP Collaborations, the LEP Electroweak Working Group, the Tevatron Electroweak Working Group, the SLD Electroweak and Heavy Flavour Working Groups, Precision electroweak measurements and constraints on the Standard Model, CERN-PH-EP/2009-023. http://www.cern.ch/LEPEWWG
  75. 75.
    J. Beringer et al. (Particle Data Group Collaboration), Phys. Rev. D 86, 010001 (2012) ADSGoogle Scholar
  76. 76.
    G. Bozzi, J. Rojo, A. Vicini, Phys. Rev. D 83, 113008 (2011). arXiv:1104.2056 [hep-ph] ADSGoogle Scholar
  77. 77.
    C. Bernaciak, D. Wackeroth, Phys. Rev. D 85, 093003 (2012). arXiv:1201.4804 [hep-ph] ADSGoogle Scholar
  78. 78.
    A. Sirlin, Phys. Rev. D 22, 971–981 (1980) ADSGoogle Scholar
  79. 79.
    W.J. Marciano, A. Sirlin, Phys. Rev. D 22, 2695 (1980) ADSGoogle Scholar
  80. 80.
    D.A. Ross, M.J.G. Veltman, Nucl. Phys. B 95, 135 (1975) ADSGoogle Scholar
  81. 81.
    M.J.G. Veltman, Acta Phys. Pol. B 8, 475 (1977) Google Scholar
  82. 82.
    M.J.G. Veltman, Nucl. Phys. B 123, 89 (1977) ADSGoogle Scholar
  83. 83.
    M.B. Einhorn, D.R.T. Jones, M.J.G. Veltman, Nucl. Phys. B 191, 146 (1981) ADSGoogle Scholar
  84. 84.
    R. Barbieri, M. Frigeni, F. Giuliani, H. Haber, Nucl. Phys. B 341, 309–321 (1990) ADSGoogle Scholar
  85. 85.
    D. Garcia, J. Solà, Mod. Phys. Lett. A 9, 211–224 (1994). Preprint UAB-FT-313 (April 1993) ADSGoogle Scholar
  86. 86.
    P.H. Chankowski et al., Nucl. Phys. B 417, 101–129 (1994). Preprint MPI-Ph/93-79 (November 1993) ADSGoogle Scholar
  87. 87.
    P. Gosdzinsky, J. Solà, Phys. Lett. B 254, 139–147 (1991) ADSGoogle Scholar
  88. 88.
    P. Gosdzinsky, J. Solà, Mod. Phys. Lett. A 6, 1943–1952 (1991) ADSGoogle Scholar
  89. 89.
    J. Grifols, J. Solà, Phys. Lett. B 137, 257 (1984) ADSGoogle Scholar
  90. 90.
    J. Grifols, J. Solà, Nucl. Phys. B 253, 47 (1985) ADSGoogle Scholar
  91. 91.
    A. Dabelstein, W. Hollik, W. Mosle, arXiv:hep-ph/9506251 (1995)
  92. 92.
    S. Heinemeyer, W. Hollik, D. Stöckinger, A.M. Weber, G. Weiglein, J. High Energy Phys. 08, 052 (2006). arXiv:hep-ph/0604147 ADSGoogle Scholar
  93. 93.
    J.R. Ellis, S. Heinemeyer, K.A. Olive, G. Weiglein, arXiv:hep-ph/0604180 (2006)
  94. 94.
    R. Benbrik, M.G. Bock, S. Heinemeyer, O. Stål, G. Weiglein et al., arXiv:1207.1096 [hep-ph] (2012)
  95. 95.
    A. Freitas, S. Heinemeyer, G. Weiglein, Nucl. Phys. Proc. Suppl. 116, 331–335 (2003). arXiv:hep-ph/0212068 ADSGoogle Scholar
  96. 96.
    G. Weiglein, Nucl. Phys. Proc. Suppl. 160, 185–189 (2006) ADSGoogle Scholar
  97. 97.
    J. Haestier, D. Stockinger, G. Weiglein, S. Heinemeyer, arXiv:hep-ph/0506259 (2005)
  98. 98.
    S. Heinemeyer, G. Weiglein, J. High Energy Phys. 10, 072 (2002). arXiv:hep-ph/0209305 ADSGoogle Scholar
  99. 99.
    S. Heinemeyer, G. Weiglein, arXiv:hep-ph/0102317 (2001)
  100. 100.
    J. van der Bij, M. Veltman, Nucl. Phys. B 231, 205 (1984) ADSGoogle Scholar
  101. 101.
    S. Heinemeyer, W. Hollik, F. Merz, S. Peñaranda, Eur. Phys. J. C 37, 481–493 (2004). arXiv:hep-ph/0403228 ADSGoogle Scholar
  102. 102.
    S. Peñaranda, S. Heinemeyer, W. Hollik, arXiv:hep-ph/0506104 (2005)
  103. 103.
    J.M. Frere, J.A.M. Vermaseren, Z. Phys. C 19, 63 (1983) ADSGoogle Scholar
  104. 104.
    S. Bertolini, Nucl. Phys. B 272, 77 (1986) ADSGoogle Scholar
  105. 105.
    W. Hollik, Z. Phys. C 32, 291 (1986) ADSGoogle Scholar
  106. 106.
    W. Hollik, Z. Phys. C 37, 569 (1988) ADSGoogle Scholar
  107. 107.
    C.D. Froggatt, R.G. Moorhouse, I.G. Knowles, Phys. Rev. D 45, 2471–2481 (1992) ADSGoogle Scholar
  108. 108.
    H.-J. He, N. Polonsky, S.-f. Su, Phys. Rev. D 64, 053004 (2001). arXiv:hep-ph/0102144 ADSGoogle Scholar
  109. 109.
    F. Mahmoudi, O. Stål, Phys. Rev. D 81, 035016 (2010). arXiv:0907.1791 [hep-ph] ADSGoogle Scholar
  110. 110.
    A. Pich, P. Tuzón, Phys. Rev. D 80, 091702 (2009). arXiv:0908.1554 [hep-ph] ADSGoogle Scholar
  111. 111.
    M. Jung, A. Pich, P. Tuzón, J. High Energy Phys. 11, 003 (2010). arXiv:1006.0470 [hep-ph] ADSGoogle Scholar
  112. 112.
    A.J. Buras, M.V. Carlucci, S. Gori, G. Isidori, J. High Energy Phys. 10, 009 (2010). arXiv:1005.5310 [hep-ph] ADSGoogle Scholar
  113. 113.
    D. López-Val, J. Solà, Phys. Rev. D 81, 033003 (2010). arXiv:0908.2898 [hep-ph] ADSGoogle Scholar
  114. 114.
    R.A. Jiménez, J. Solà, Phys. Lett. B 389, 53–61 (1996). arXiv:hep-ph/9511292 ADSGoogle Scholar
  115. 115.
    J.A. Coarasa, R.A. Jimenez, J. Solà, Phys. Lett. B 389, 312–320 (1996). arXiv:hep-ph/9511402 ADSGoogle Scholar
  116. 116.
    M.S. Carena, H.E. Haber, Prog. Part. Nucl. Phys. 50, 63–152 (2003). arXiv:hep-ph/0208209 ADSGoogle Scholar
  117. 117.
    S. Heinemeyer, Acta Phys. Pol. B 39, 2673–2692 (2008). arXiv:0807.2514 [hep-ph] ADSGoogle Scholar
  118. 118.
    A. Djouadi, Phys. Rep. 459, 1–241 (2008). arXiv:hep-ph/0503173 [hep-ph] ADSGoogle Scholar
  119. 119.
    H. Flacher et al., Eur. Phys. J. C 60, 543–583 (2009). arXiv:0811.0009 [hep-ph] ADSGoogle Scholar
  120. 120.
    S.R. Juárez, D. Morales, P. Kielanowski, arXiv:1201.1876 [hep-ph] (2012)
  121. 121.
    F. Mahmoudi, Comput. Phys. Commun. 178, 745–754 (2008). arXiv:0710.2067 [hep-ph] ADSzbMATHGoogle Scholar
  122. 122.
    F. Mahmoudi, Comput. Phys. Commun. 180, 1579–1613 (2009). arXiv:0808.3144 [hep-ph] ADSGoogle Scholar
  123. 123.
    A.W. El Kaffas, P. Osland, O.M. Ogreid, Phys. Rev. D 76, 095001 (2007). arXiv:0706.2997 [hep-ph] ADSGoogle Scholar
  124. 124.
    A.W. El Kaffas, P. Osland, O.M. Ogreid, Nonlinear Phenom. Complex Syst. 10, 347–357 (2007). arXiv:hep-ph/0702097 Google Scholar
  125. 125.
    A. Azatov, S. Chang, N. Craig, J. Galloway, arXiv:1206.1058 [hep-ph] (2012)
  126. 126.
    D. Carmi, A. Falkowski, E. Kuflik, T. Volansky, J. Zupan, arXiv:1207.1718 [hep-ph] (2012)
  127. 127.
    D. Eriksson, J. Rathsman, O. Stål, Comput. Phys. Commun. 181, 189–205 (2010). arXiv:0902.0851 [hep-ph] ADSzbMATHGoogle Scholar
  128. 128.
    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, Comput. Phys. Commun. 181, 138–167 (2010). arXiv:0811.4169 [hep-ph] ADSzbMATHGoogle Scholar
  129. 129.
    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein, K.E. Williams, Comput. Phys. Commun. 182, 2605–2631 (2011). arXiv:1102.1898 [hep-ph] ADSGoogle Scholar
  130. 130.
    G. Ferrera, J. Guasch, D. López-Val, J. Solà, Phys. Lett. B 659, 297–307 (2008). arXiv:0707.3162 [hep-ph] ADSGoogle Scholar
  131. 131.
    G. Ferrera, J. Guasch, D. López-Val, J. Solà, PoS RADCOR2007, 043 (2007). arXiv:0801.3907 [hep-ph]
  132. 132.
    A. Arhrib, R. Benbrik, C.-W. Chiang, Phys. Rev. D 77, 115013 (2008). arXiv:0802.0319 [hep-ph] ADSGoogle Scholar
  133. 133.
    R.N. Hodgkinson, D. López-Val, J. Solà, Phys. Lett. B 673, 47–56 (2009). arXiv:0901.2257 [hep-ph] ADSGoogle Scholar
  134. 134.
    N. Bernal, D. López-Val, J. Solà, Phys. Lett. B 677, 39–47 (2009). arXiv:0903.4978 [hep-ph] ADSGoogle Scholar
  135. 135.
    D. López-Val, J. Solà, Phys. Lett. B 702, 246–255 (2011). arXiv:1106.3226 [hep-ph] ADSGoogle Scholar
  136. 136.
    J. Solà, D. López-Val, Nuovo Cimento C 34S1, 57–67 (2011). arXiv:1107.1305 [hep-ph] Google Scholar
  137. 137.
    F. Cornet, W. Hollik, Phys. Lett. B 669, 58–61 (2008). arXiv:0808.0719 [hep-ph] ADSGoogle Scholar
  138. 138.
    E. Asakawa, D. Harada, S. Kanemura, Y. Okada, K. Tsumura, Phys. Lett. B 672, 354–360 (2009). arXiv:0809.0094 [hep-ph] ADSGoogle Scholar
  139. 139.
    A. Arhrib, R. Benbrik, C.-H. Chen, R. Santos, Phys. Rev. D 80, 015010 (2009). arXiv:0901.3380 [hep-ph] ADSGoogle Scholar
  140. 140.
    E. Asakawa, D. Harada, S. Kanemura, Y. Okada, K. Tsumura, Phys. Rev. D 82, 115002 (2010). arXiv:1009.4670 [hep-ph] ADSGoogle Scholar
  141. 141.
    A. Arhrib, G. Moultaka, Nucl. Phys. B 558, 3–40 (1999). arXiv:hep-ph/9808317 ADSGoogle Scholar
  142. 142.
    J. Guasch, W. Hollik, A. Kraft, Nucl. Phys. B 596, 66–80 (2001) ADSGoogle Scholar
  143. 143.
    D. López-Val, J. Solà, in PoS RADCOR2009 (2010), p. 045. arXiv:1001.0473 [hep-ph] Google Scholar
  144. 144.
    J. Solà, D. López-Val, Fortschr. Phys. 58, 660–664 (2010) Google Scholar
  145. 145.
    M. Consoli, W. Hollik, F. Jegerlehner, Phys. Lett. B 227, 167 (1989) ADSGoogle Scholar
  146. 146.
    A. Freitas, W. Hollik, W. Walter, G. Weiglein, Nucl. Phys. B 632, 189–218 (2002). arXiv:hep-ph/0202131 ADSGoogle Scholar
  147. 147.
    M. Awramik, M. Czakon, Phys. Rev. Lett. 89, 241801 (2002). arXiv:hep-ph/0208113 ADSGoogle Scholar
  148. 148.
    M. Awramik, M. Czakon, A. Onishchenko, O. Veretin, Phys. Rev. D 68, 053004 (2003). arXiv:hep-ph/0209084 ADSGoogle Scholar
  149. 149.
    M. Awramik, M. Czakon, Phys. Lett. B 568, 48–54 (2003). arXiv:hep-ph/0305248 [hep-ph] ADSGoogle Scholar
  150. 150.
    M. Awramik, M. Czakon, A. Freitas, G. Weiglein, Phys. Rev. D 69, 053006 (2004). arXiv:hep-ph/0311148 [hep-ph] ADSGoogle Scholar
  151. 151.
    M. Awramik, M. Czakon, A. Freitas, G. Weiglein, Phys. Rev. D 69, 053006 (2004). arXiv:hep-ph/0311148 [hep-ph] ADSGoogle Scholar
  152. 152.
    A. Onishchenko, O. Veretin, Phys. Lett. B 551, 111–114 (2003). arXiv:hep-ph/0209010 ADSGoogle Scholar
  153. 153.
    J.J. van der Bij, K.G. Chetyrkin, M. Faisst, G. Jikia, T. Seidensticker, Phys. Lett. B 498, 156–162 (2001). arXiv:hep-ph/0011373 ADSGoogle Scholar
  154. 154.
    W. Grimus, L. Lavoura, O.M. Ogreid, P. Osland, J. Phys. G 35, 075001 (2008). arXiv:0711.4022 [hep-ph] ADSGoogle Scholar
  155. 155.
    W. Grimus, L. Lavoura, O. Ogreid, P. Osland, Nucl. Phys. B 801, 81–96 (2008). arXiv:0802.4353 [hep-ph] ADSGoogle Scholar
  156. 156.
    T. Hahn, Comput. Phys. Commun. 140, 418 (2001). arXiv:hep-ph/0012260 ADSzbMATHGoogle Scholar
  157. 157.
    A. Djouadi, C. Verzegnassi, Phys. Lett. B 195, 265 (1987) ADSGoogle Scholar
  158. 158.
    A. Djouadi, Nuovo Cimento A 100, 357 (1988) ADSGoogle Scholar
  159. 159.
    B.A. Kniehl, Nucl. Phys. B 347, 86–104 (1990) ADSGoogle Scholar
  160. 160.
    F. Halzen, B.A. Kniehl, Nucl. Phys. B 353, 567–590 (1991) ADSGoogle Scholar
  161. 161.
    B.A. Kniehl, A. Sirlin, Nucl. Phys. B 371, 141–148 (1992) ADSGoogle Scholar
  162. 162.
    B.A. Kniehl, A. Sirlin, Phys. Rev. D 47, 883–893 (1993) ADSGoogle Scholar
  163. 163.
    S. Fanchiotti, B.A. Kniehl, A. Sirlin, Phys. Rev. D 48, 307–331 (1993). arXiv:hep-ph/9212285 [hep-ph] ADSGoogle Scholar
  164. 164.
    A. Djouadi, P. Gambino, Phys. Rev. D 49, 3499–3511 (1994). arXiv:hep-ph/9309298 [hep-ph] ADSGoogle Scholar
  165. 165.
    L. Avdeev, J. Fleischer, S. Mikhailov, O. Tarasov, Phys. Lett. B 336, 560–566 (1994). arXiv:hep-ph/9406363 [hep-ph] ADSGoogle Scholar
  166. 166.
    K. Chetyrkin, J.H. Kuhn, M. Steinhauser, Phys. Rev. Lett. 75, 3394–3397 (1995). arXiv:hep-ph/9504413 [hep-ph] ADSGoogle Scholar
  167. 167.
    K. Chetyrkin, J.H. Kuhn, M. Steinhauser, Nucl. Phys. B 482, 213–240 (1996). arXiv:hep-ph/9606230 [hep-ph] ADSGoogle Scholar
  168. 168.
    B.W. Lee, C. Quigg, H.B. Thacker, Phys. Rev. Lett. 38, 883–885 (1977) ADSGoogle Scholar
  169. 169.
    B.W. Lee, C. Quigg, H. Thacker, Phys. Rev. D 16, 1519 (1977) ADSGoogle Scholar
  170. 170.
    A. Arhrib, arXiv:hep-ph/0012353 (2000)
  171. 171.
    A.G. Akeroyd, A. Arhrib, E.-M. Naimi, Phys. Lett. B 490, 119 (2000). arXiv:hep-ph/0006035 ADSGoogle Scholar
  172. 172.
    S. Kanemura, T. Kubota, E. Takasugi, Phys. Lett. B 313, 155–160 (1993). arXiv:hep-ph/9303263 ADSGoogle Scholar
  173. 173.
    J. Maalampi, J. Sirkka, I. Vilja, Phys. Lett. B 265, 371–376 (1991) ADSGoogle Scholar
  174. 174.
    A.G. Akeroyd, A. Arhrib, E.-M. Naimi, Phys. Lett. B 490, 119–124 (2000). arXiv:hep-ph/0006035 ADSGoogle Scholar
  175. 175.
    I.F. Ginzburg, I.P. Ivanov, Phys. Rev. D 72, 115010 (2005). arXiv:hep-ph/0508020 ADSGoogle Scholar
  176. 176.
    P. Osland, P.N. Pandita, L. Selbuz, Phys. Rev. D 78, 015003 (2008). arXiv:0802.0060 [hep-ph] ADSGoogle Scholar
  177. 177.
    G. ’t Hooft, M. Veltman, Nucl. Phys. B 44, 189–213 (1972) ADSGoogle Scholar
  178. 178.
    T. Hahn, M. Pérez-Victoria, Comput. Phys. Commun. 118, 153–165 (1999). arXiv:hep-ph/9807565 ADSGoogle Scholar
  179. 179.
    T. Hahn, M. Rauch, Nucl. Phys. Proc. Suppl. 157, 236–240 (2006). arXiv:hep-ph/0601248 [hep-ph] ADSGoogle Scholar
  180. 180.
    M. Frank et al., J. High Energy Phys. 02, 047 (2007). arXiv:hep-ph/0611326 ADSGoogle Scholar
  181. 181.
    G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich, G. Weiglein, Eur. Phys. J. C 28, 133–143 (2003). arXiv:hep-ph/0212020 ADSGoogle Scholar
  182. 182.
    S. Heinemeyer, W. Hollik, G. Weiglein, Eur. Phys. J. C 9, 343–366 (1999). arXiv:hep-ph/9812472 ADSGoogle Scholar
  183. 183.
    S. Heinemeyer, W. Hollik, G. Weiglein, Comput. Phys. Commun. 124, 76–89 (2000). arXiv:hep-ph/9812320 ADSzbMATHGoogle Scholar
  184. 184.
    A. Arbey, M. Battaglia, A. Djouadi, F. Mahmoudi, arXiv:1207.1348 [hep-ph] (2012)
  185. 185.
    T. Electroweak, Working Group and CDF and D0 Collaborations. FERMILAB-TM-2504-E, CDF-NOTE-10549, D0-NOTE-6222. arXiv:1107.5255 [hep-ex]
  186. 186.
    M. Awramik, M. Czakon, Nucl. Phys. Proc. Suppl. 116, 238–242 (2003). arXiv:hep-ph/0211041 [hep-ph] ADSGoogle Scholar
  187. 187.
    A. Freitas, W. Hollik, W. Walter, G. Weiglein, Phys. Lett. B 495, 338–346 (2000). arXiv:hep-ph/0007091 [hep-ph] ADSGoogle Scholar
  188. 188.
    M. Faisst, J.H. Kuhn, T. Seidensticker, O. Veretin, Nucl. Phys. B 665, 649–662 (2003). arXiv:hep-ph/0302275 ADSGoogle Scholar
  189. 189.
    R. Boughezal, J.B. Tausk, J.J. van der Bij, Nucl. Phys. B 713, 278–290 (2005). arXiv:hep-ph/0410216 ADSGoogle Scholar
  190. 190.
    Y. Schroder, M. Steinhauser, Phys. Lett. B 622, 124–130 (2005). arXiv:hep-ph/0504055 ADSGoogle Scholar
  191. 191.
    K.G. Chetyrkin, M. Faisst, J.H. Kuhn, P. Maierhofer, C. Sturm, Phys. Rev. Lett. 97, 102003 (2006). arXiv:hep-ph/0605201 ADSGoogle Scholar
  192. 192.
    R. Boughezal, M. Czakon, Nucl. Phys. B 755, 221–238 (2006). arXiv:hep-ph/0606232 ADSGoogle Scholar
  193. 193.
    O. Buchmüller, R. Cavanaugh, A. De Roeck, J. Ellis, H. Flacher et al., Phys. Rev. D 81, 035009 (2010). arXiv:0912.1036 [hep-ph] ADSGoogle Scholar
  194. 194.
    J.A. Evans, M.A. Luty, Phys. Rev. Lett. 103, 101801 (2009). arXiv:0904.2182 [hep-ph] ADSGoogle Scholar
  195. 195.
    J.A. Coarasa, D. Garcia, J. Guasch, R.A. Jiménez, J. Solà, Eur. Phys. J. C 2, 373–392 (1998). arXiv:hep-ph/9607485 ADSGoogle Scholar
  196. 196.
    M.S. Carena, D. Garcia, U. Nierste, C.E.M. Wagner, Nucl. Phys. B 577, 88–120 (2000). arXiv:hep-ph/9912516 ADSGoogle Scholar
  197. 197.
    J. Guasch, J. Solà, W. Hollik, Phys. Lett. B 437, 88–99 (1998). arXiv:hep-ph/9802329 ADSGoogle Scholar
  198. 198.
    A. Belyaev, D. Garcia, J. Guasch, J. Solà, Phys. Rev. D 65, 031701 (2002). arXiv:hep-ph/0105053 ADSGoogle Scholar
  199. 199.
    S. Béjar, J. Guasch, D. López-Val, J. Solà, Phys. Lett. B 668, 364–372 (2008). arXiv:0805.0973 [hep-ph] ADSGoogle Scholar
  200. 200.
    S. Béjar, J. Guasch, D. López-Val, J. Solà, Phys. Rev. D 81, 113005 (2010). arXiv:1003.4312 [hep-ph] ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2013

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikUniversität HeidelbergHeidelbergGermany
  2. 2.Dept. Estructura i Constituents de la MatèriaUniversitat de BarcelonaBarcelonaSpain
  3. 3.Institut de Ciències del CosmosBarcelonaSpain

Personalised recommendations